Multivalued Elliptic Equation with exponential critical growth in ℝ²

2016/01/20 by Claudianor O. Alves, Alves, Claudianor O., Jefferson A. Santos +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1601.05286

arxiv created 2016/01/20 · arxiv updated 2016/01/21

Abstract

In this work we study the existence of nontrivial solution for the following class of multivalued elliptic problems -Δu+V(x)u-εh(x)∈ ∂_t F(x,u) in ℝ², \eqno(P) where ε>0, V is a continuous function verifying some conditions, h ∈ (H¹(ℝ²))^* and ∂_t F(x,u) is a generalized gradient of F(x,t) with respect to t and F(x,t)=∫₀^tf(x,s) ds. Assuming that f has an exponential critical growth and a discontinuity point, we have applied Variational Methods for locally Lipschitz functional to get two solutions for (P) when ε is small enough.

Related

• On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth
• Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in ℝ²
• Existence and Multiplicity for elliptic p-Laplacian problems with\n critical growth in the gradient
• Critical fractional elliptic equations with exponential growth without Ambrosetti-Rabinowitz type condition
• A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient